Square-Root Regret Bounds for Continuous-Time Episodic Markov Decision Processes

• 成果类型: Article
• 署名作者: Gao, Xuefeng; Zhou, Xunyu
• 署名单位: Chinese University of Hong Kong; Columbia University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X; 1526-5471
• DOI: 10.1287/moor.2022.0283
• 发表日期: 2026-02
• 关键词: continuous time Markov decision processes; Regret Bounds; Reinforcement Learning; episodic; finite-horizon; state

摘要

We study reinforcement learning for continuous-time Markov decision processes (MDPs) in the finite-horizon episodic setting. In contrast to discrete-time MDPs, the intertransition times of a continuous-time MDP are exponentially distributed with rate parameters depending on the state-action pair at each transition. We present a learning algorithm based on the methods of value iteration and upper confidence bound. We derive an upper bound on the worst case expected regret for the proposed algorithm and establish a worst case lower bound with both bounds of the order of square root on the number of episodes. Finally, we conduct simulation experiments to illustrate the performance of our algorithm.